Question

Which of the following statements is true about the unknown leg length? Select all that apply.

A) The equation ((734)² + 9 = c²) will find the unknown leg length.
B) The equation ((334)² + 6² = 92²) will find the unknown leg length.
C) The equation (a² + (134)² = 92²) will find the unknown leg length.
D) The length of the unknown leg is (√115) m.
E) The length of the unknown leg is 47 m.

Answer 1

The correct statement about the unknown leg length is that the equation (a² + (134)² = 92²) will find the unknown leg length.

Step-by-step explanation:

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as a² + b² = c², where a and b are the lengths of the legs of the triangle, and c is the length of the hypotenuse.

Based on this information, we can determine which statements are true about the unknown leg length:

1. Statement A): The equation ((734)² + 9 = c²) is incorrect because it does not follow the correct form of the Pythagorean theorem.
2. Statement B): The equation ((334)² + 6² = 92²) is incorrect because it also does not follow the correct form of the Pythagorean theorem.
3. Statement C): The equation (a² + (134)² = 92²) is correct and will find the unknown leg length.
4. Statement D): The length of the unknown leg is not (√115) m because this value does not match any of the given equations or options.
5. Statement E): The length of the unknown leg is not 47 m because this value does not match any of the given equations or options.

Therefore, the correct statements about the unknown leg length are A) The equation (a² + (134)² = 92²) will find the unknown leg length.